MinT - Best Known (67, 67+25, s)-Nets in Base 2

Best Known (67, 67+25, s)-Nets in Base 2

(67, 67+25, 84)-Net over F₂ — Constructive and digital

Digital (67, 92, 84)-net over F₂, using

1 times m-reduction [i] based on digital (67, 93, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 31, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(67, 67+25, 124)-Net over F₂ — Digital

Digital (67, 92, 124)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+25, 996)-Net in Base 2 — Upper bound on s

There is no (67, 92, 997)-net in base 2, because

1 times m-reduction [i] would yield (67, 91, 997)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2477 396015 895596 539026 803068 > 2⁹¹ [i]